A long string is constructed by joining the ends of two shorter strings.The tension in the strings is the same but string I has 4 times the linear mass density of string II.When a sinusoidal wave passes from string I to string II:
A)the frequency decreases by a factor of 4
B)the frequency decreases by a factor of 2
C)the wavelength decreases by a factor of 4
D)the wavelength decreases by a factor of 2
E)the wavelength increases by a factor of 2

Question

Quizplus · Accepted Answer

When the wave passes from string I to II, the speed of the wave changes due to the change in linear mass density. Since the tension is the same in both strings, the speed of the wave is proportional to the square root of the linear mass density. Therefore, the wave speed in string II is half that of string I. As wavelength is inversely proportional to frequency for a wave of constant speed, the wavelength decreases by a factor of 2 when the wave passes from string I to II.

A Long String Is Constructed by Joining the Ends of Two